Do these FOL formula both represent "You can fool some of the people all of the time"?
(1) can be paraphrased as &quot;There exists an x, and for any t if x is a person and t is a time, then x can be fooled at time t&quot; (I would use fool-able instead of can-fool, as it is closer to the intended meaning).
(2) would be &quot;There exists an x, and for any t, you can fool x is a person and t is a time.&quot;
They are not equivalent: person(x)  and time(t) are boolean predicates, which return a truth value: they are true if x is a person, and t is a time, respectively. So in (1) they act as a constraint on the values that x and t can take. If x was a saucepan, then person(x) would be false, and thus you wouldn't be able to claim that you can fool a saucepan.
So can-fool takes two arguments: one for which person is true, and one for which time is true. But in (2), the arguments are actually the boolean truth values: if x was &quot;Falstaff&quot; and t was &quot;yesterday&quot;, then in (1) the premise would be true, as person(&quot;Falstaff&quot;) and time(&quot;yesterday&quot;) are true, and so you conclude can-fool(&quot;Falstaff&quot;, &quot;yesterday&quot;).
In (2) that becomes can-fool(person(&quot;Falstaff&quot;), time(&quot;yesterday&quot;)), which evaluates to can-fool(true, true), and that won't work.